Kummer Rigidity for Hyperbolic Hyperkähler Automorphisms
Date:
A talk in Third BiSTRO-mini-conference.
Abstract
Dynamical systems that have volume-class measures of maximal entropy typically have locally homogeneous structures. In complex dynamics, this usually means that the automorphism comes from a torus, as established by Zdunik, Berteloot–Dupont, Cantat–Dupont, Filip–Tosatti, and others. As a successor to this series, we present another result that applies to projective hyperkahler manifolds, a higher-dimensional analogue of K3 surfaces.
We discuss how such a system has a surprisingly simple dynamical structure, and how we can make use of this structure to identify the given automorphism as a “Kummer example” with a (Ricci-flat) flat metric. All the necessary background will be provided.